Consider the function defined on the closed interval .

MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Consider the function

g(x)=\sqrt{25-x^{2}}

defined on the closed interval

[-5,5]

. (i) State the domain of

g

and identify the endpoints of the interval under consideration. (ii) Determine whether there exist any points in

(-5,5)

at which

g'(x)=0

. Justify your answer without performing explicit derivative calculations. (iii) Using clear reasoning, identify the points in

[-5,5]

where

g

attains its absolute maximum and absolute minimum values. State these maximum and minimum values.